Understanding Derivatives of Composite Functions

The video tutorial explains how to find the derivative of a composite function involving sine, natural log, and x squared. It breaks down the process using the chain rule, defining each function involved, and simplifying the derivative step by step. The tutorial emphasizes understanding the chain rule and applying it to nested functions, ultimately simplifying the expression to a manageable form.

What is the main function we are trying to differentiate in this tutorial?

• Sine of the natural log of x squared

• x squared

• Natural log of x

• Sine of x

Which rule is primarily used to differentiate composite functions?

• Chain Rule

• Quotient Rule

• Power Rule

• Product Rule

What is the derivative of sine with respect to its inner function?

• x squared

• Sine of x

• Cosine of x

• Natural log of x

When applying the chain rule to the natural log function, what is the derivative of ln(x)?

• ln(x)

• x

• x squared

• 1/x

In the context of this problem, what is g prime of x squared?

• 1/x

• 1/x squared

• x

• 2x

What is the derivative of x squared with respect to x?

• 1/x

• x squared

• 2x

• x

Tags

CCSS.HSA.APR.D.6

How do we simplify the expression 2x over x squared?

• x

• 2x

• 2 over x

• x squared

What is the final simplified form of the derivative?

• 2x times cosine of natural log of x squared

• 2 over x times cosine of natural log of x squared

• Natural log of x squared

• Cosine of x squared

What is the purpose of using the chain rule in this context?

• To differentiate simple functions

• To solve algebraic equations

• To integrate functions

• To handle composite functions

What analogy is used to describe the process of differentiating composite functions?

• Climbing a mountain

• Building a house

• Solving a puzzle

• Peeling an onion